Atlas3,627 of 3,915

Choreography SC.35

From Simó (2001)

Choreography SC.35 is a periodic orbit of the planar three-body problem: three equal masses that return to their starting positions and velocities every 6.7949 time units, published by Simó (2001). Carles Simó’s catalogue of three-body choreographies with nonzero angular momentum, the curves that made choreographies famous. All unstable except the figure-eight. It is unstable (largest Floquet multiplier 30313), so a small nudge makes it unravel over a few periods. The bodies pass within 0.0195 of each other at a top speed of 7.72, line up 18 times a period, and the computed loop closes to 1.2×10⁻²⁶.

Measured over one period

Period: 6.794938915
Masses: 1 : 1 : 1
Energy: -4.50000
Angular momentum: 1.0060
Closest approach: 0.01953
Top speed: 7.725
Path length: 31.662
Alignments per period: 18
Stability: unstable (|λ|max 3.0×10¹⁸)
Loop closure: 1.2×10⁻²⁶

Neighbours on the map

All Simó’s choreographies, the families of periodic three-body orbits, or the atlas map.